The Matrix de Burlacu Denisa şi Balaci Marco este licenţiat printr-o Licenţă Creative Commons Atribuire 4.0 Internațional .
Time in Math
-The Matrix-
Students:
Burlacu Denisa
Balaci Marco
Coordinating teachers:
Gosa Şimona
Neamţu Mihai
A
-History-
The beginnings of matrices and determinants date back to the 2nd century BC. although traces can be seen as early as the 4th century BC. However, they did not exist until the end of the 17th century when the idea reappeared and developed.
The idea of determinant appeared in Japan and Europe at about the same time. Seki (a Japanese mathematician who lived between 1642 and 1708) was the first to publish in 1683 "Methods of Solving Concealed Problems.“
In the same year, 1683, the determinants appeared in Europe and at the same time Leibniz (German mathematician who lived between 1646-1716) wrote to L’Hospital that the system of 3 equations
10 + 11x + 12y = 0
20 + 21x + 22y = 0
30 + 31x + 32y = 0
has a solution because 10 · 21 · 32 + 11 · 22 · 30 + 20 · 31 · 12 = 10 · 22 · 31 + 11 · 20 · 32 + 12 · 21 · 30which is the condition that the coefficient matrix has the determinant 0.
B
-The inverse of the matrix-
~Cryptography~
Cryptography, or cryptology, is the practice and study of techniques for secure communication in the presence of adversarial behavior. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages; various aspects in information security such as data confidentiality, data integrity, authentication, and non-repudiation are central to modern cryptography.
One method used in cryptology is the encoding of the matrices.
In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra.
Today governments use sophisticated methods of coding and decoding messages. One type of code, which is extremely difficult to break, makes use of a large matrix to encode a message. The receiver of the message decodes it using the inverse of the matrix. This first matrix is called the encoding matrix and its inverse is called the decoding matrix.
C
-Example-
So the message becomes:
�
D
-Encoding-
E
-Decoding-
F
~Thank you!~
Bibliography:
https://en.wikipedia.org/wiki/Cryptography
https://en.wikipedia.org/wiki/Matrix_(mathematics)
https://mathshistory.st-andrews.ac.uk/HistTopics/Matrices_and_determinants/
https://pixabay.com/illustrations/time-matrix-network-digital-1995539/